Geophysical hazards stress urban social, economic and political systems, but many studies focus on single locations over short periods. The manner in which a natural disaster propagates across cities globally through urban trade networks remains unexplored. Starting from a novel empirical baseline model for global production and trade, here we develop a dynamical model for the spread of individual cyclone impacts across the world's cities. We find that cities are vulnerable to economic harm even if they are geographically distant from the location of direct impacts of cyclones. These adverse secondary impacts are responsible for up to three-fourths of the effects of the largest storms and are generated primarily by cyclone exposure in North America and East Asia, in part because of the roles of these regions as principal purchasers and suppliers, respectively, of industrial materials. Vulnerability to adverse secondary impacts of cyclones is highest in cities that are strongly dependent on the global trade network but have relatively few suppliers. Our results suggest that, in addition to improvements in protective infrastructure, urban adaptation to storm damage and climate change might require modifications to trade network linkages. Hazards affect more than the area originally hit. This study finds cities distant from cyclones may still be vulnerable to secondary impacts through their trade networks.

Spatial patterning of coral reef sessile benthic organisms can constrain competitive and demographic rates, with implications for dynamics over a range of time scales. However, techniques for quantifying and analysing reefscape behaviour, particularly at short to intermediate time scales (weeks to decades), are lacking. An analysis of the dynamics of coral reefscapes simulated with a lattice model shows consistent trends that can be categorized into four stages: a repelling stage that moves rapidly away from an unstable initial condition, a transient stage where spatial rearrangements bring key competitors into contact, an attracting stage where the reefscape decays to a steady-state attractor, and an attractor stage. The transient stage exhibits nonlinear dynamics, whereas the other stages are linear. The relative durations of the stages are affected by the initial spatial configuration as characterized by coral aggregation—a measure of spatial clumpiness, which together with coral and macroalgae fractional cover, more completely describe modelled reefscape dynamics. Incorporating diffusional processes results in aggregated patterns persisting in the attractor. Our quantitative characterization of reefscape dynamics has possible applications to other spatio-temporal systems and implications for reef restoration: high initial aggregation patterns slow losses in herbivore-limited systems and low initial aggregation configurations accelerate growth in herbivore-dominated systems.

The fundamental and dominant process operating in all ice‐wedge networks is thermal contraction fracturing. This assumption forms the basis of a numerical model combining fracture initiation and propagation in frozen ground and ice, influence of open fractures on stresses, growth of ice wedges and ground deformation above wedges (Plug and Werner, 2001 , 2002 ). Modelled polygonal networks self‐organise through interactions between fractures, stress and re‐fracture in ice wedges. The resultant polygonal form feeds back on fracturing in individual ice wedges. Spacing, wedge width and fracture frequency in wedges do not reflect mean climate parameters, but instead are sensitive to infrequent climate events and initial conditions, and may vary even under stationary climate — meaning that ice‐wedge casts are difficult to use as estimators of past climate. Burn ( 2004 ) suggested that that some of the assumptions underlying the model are incorrect in that they either misrepresent field conditions or ignore crucial site‐specific factors. These criticisms misread and invert the goal of our work, shared in part by any modelling exercise or field investigation, which is to elucidate common, robust behaviours and characteristics across a range of sites rather than to reproduce or describe in precise terms a particular instance. Copyright © 2007 John Wiley & Sons, Ltd.

The fate of coastlines and their human settlements under the effects of global climate change will depend critically on the nonlinear dynamics of and feedbacks between shoreline processes and human agency. This hypothesis is explored on the barrier island coastline of Ocean City and Assateague Island National Seashore, Maryland, using a model‐coupling natural coastal processes, including erosion, accretion, island overwash, alongshore sediment transport, dune growth and migration, inlet migration and ebb tidal delta growth to economics of tourist resort development through storm damage and beach and dune replenishment. Initiating the model in 1845, the RMS difference between model and measurements of the shoreline position in 2001 is 84.97 m compared to a net onshore migration of 472.2 m and the RMS difference between modeled and measured hotel room density in 2001 is 2950 rooms km −1 compared to a net gain of 28,824 rooms km −1 . Simulations to year 3400 for a rate of sea level rise of 3.5 mm a −1 show a steady state barrier island position 158 m further offshore and 0.54 m lower in elevation compared to its natural counterpart. Changing the rate of sea level rise to 10.5 mm a −1 increases these differences to 288 m and 0.76 m. Changing storminess by increasing the standard deviation of storm size 50% diminishes coupling between resorts and barriers, bringing the natural and coupled attractors into near coincidence. These results suggest that predicted increases in the rate of sea level rise will lead to enhanced vulnerability for Ocean City.

Two existing models for bed form orientation are tested against measurements of megaripple crest line orientation from Scripps Beach. Optical time‐averaged images of the surf zone sand bed at 10 min intervals are processed with an automatic crest line tracing algorithm. Flow measurements concurrent with images of the sand bed collected during 3–7 April and 17–23 July 1999 are used as input to the gross bed form normal transport model (bed forms align to maximize gross transport across crests) predicting steady state crest orientation and the defect model (bed forms reorient at a rate proportional to the differential velocity of crest line ends, or defects) predicting a time‐dependent orientation. Generally poor agreement was found between predictions and measurements of crest line orientation. The gross bed form normal transport model predicted crest line normal orientation within 20° of measured orientation for 38% of records, with increased agreement coinciding with longitudinal and oblique bed forms. The defect model predicted crest line normal orientation within 20° of measurements for 22% of records when the ratio between defect and transport event timescales is assumed ≫1 and 14% of the records for the ratio ≪1. Although migration and mean sediment transport direction are assumed to coincide in both models, RMS deviation in bed form migration direction from the calculated 30 min mean sediment transport direction was found to be 38°. Additionally, RMS deviation of megaripple migration direction from crest line normal orientation was 39°.

As humans increasingly occupy and modify marginal landscapes, previously unobserved long timescale, emergent behaviors related to interactions between natural processes and human agency are possible. Barrier islands, which are low‐lying strips of sand separated from a coast by lagoons, cut by inlets and topped by sand dunes, have been significantly modified through the development of tourist resorts. Resorts and barrier islands are dynamically coupled through storm damage and beach erosion, and measures taken to prevent or mitigate them. In response to rising sea level, a natural barrier island migrates steadily up the continental shelf. In contrast, we show that in a novel numerical model‐coupling barrier island processes with resort development, storm damage, and hazard mitigation, policy decisions driven by market dynamics destabilize barrier island response to rising sea level, giving rise to emergent, episodic boom and bust cycles, which alternate in phase alongshore, and less frequent, regionally extensive resort destruction events. Developed barrier islands are precariously maintained at lower elevations and further offshore than their natural counterparts, a situation exacerbated by insurance, which can lead to island inundation. Our results suggest that coastal areas that have recently instituted protection measures eventually will experience a widespread upsurge in damage if these practices are sustained, even in the absence of climate‐change‐induced increased storminess.

A preliminary dynamical analysis of landscapes and humans as hierarchical complex systems suggests that strong coupling between the two that spreads to become regionally or globally pervasive should be focused at multi-year to decadal time scales. At these scales, landscape dynamics is dominated by water, sediment and biological routing mediated by fluvial, oceanic, atmospheric processes and human dynamics is dominated by simplifying, profit-maximizing market forces and political action based on projection of economic effect. Also at these scales, landscapes impact humans through patterns of natural disasters and trends such as sea level rise; humans impact landscapes by the effect of economic activity and changes meant to mitigate natural disasters and longer term trends. Based on this analysis, human-landscape coupled systems can be modeled using heterogeneous agents employing prediction models to determine actions to represent the nonlinear behavior of economic and political systems and rule-based routing algorithms to represent landscape processes. A cellular model for the development of New Orleans illustrates this approach, with routing algorithms for river and hurricane-storm surge determining flood extent, five markets (home, labor, hotel, tourism and port services) connecting seven types of economic agents (home buyers/laborers, home developers, hotel owners/ employers, hotel developers, tourists, port services developer and port services owners/employers), building of levees or a river spillway by political agents and damage to homes, hotels or port services within cells determined by the passage or depth of flood waters. The model reproduces historical aspects of New Orleans economic development and levee construction and the filtering of frequent small-scale floods at the expense of large disasters.

An abstracted model for saturated surf zone megaripple occurrence, based on the hypothesis that megaripples form and persist unless flow conditions change too rapidly or the bed passes through the swash zone, correctly predicts the bed state (presence or absence of megaripples) for 73% of measurements over 1 year at Scripps Beach, more than seven standard deviations above the agreement between a random model and the measurements. Transitions between bed states are predicted within 1.5 hours for 54% of measurements, compared with 6% agreement for a random model. The model is forced with a record of water depth over the beach, H (from offshore tide measurements and inferred changes in bed elevation), assuming that changes in flow conditions and depth are determined by tide level alone in a saturated surf zone. Model parameter values are estimated independent of model results: megaripple formation time, T = 2.5 hours; maximum RMS depth change over time T, ΔHRMS* = 0.1 m; and minimum depth (averaged over time T) below which megaripples are smoothed, Hsw = 0.3 m. Allowing model parameters to vary increases agreement between measurements and model predictions to a maximum 82% for parameter values T = 3 hours, ΔHRMS* = 0.05 m, and Hsw = 0.1 m. Neither bed state nor bed state transitions are correlated with offshore wave conditions.

Field measurements of morphology and swash flow during three episodes of beach cusp development indicate that tides modulate the height and cross‐shore position of beach cusps. During rising tide, beach cusp height decreases as embayments accrete more than horns and the cross‐shore extent of beach cusps decreases. During falling tide, beach cusp height increases as embayments erode more than horns and cross‐shore extent increases. A numerical model for beach cusp formation based on self‐organization, extended to include the effects of morphological smoothing seaward of the swash front and infiltration into the beach, reproduces the observed spacing, position, and tidal modulation. During rising tide, water particles simulating swash infiltrate, preferentially in embayments, causing enhanced deposition. During falling tide, exfiltration of water particles combined with diversion of swash from horns causes enhanced erosion in embayments. Smoothing of beach morphology in the swash zone seaward of the swash front and in the shallow surf zone accounts for most of the observed tidal modulation, even in the absence of infiltration and exfiltration. Despite the qualitative, and in some cases quantitative, agreement of the model and measurements, the model fails to reproduce observed large deviations of horn orientation from shore normal, some aspects of beach cusp shape, and deviations from the basic tidal modulation, possibly because of the simplified parameterization of cross‐shore sediment transport and the neglect of the effects of sea surface gradients on flow.

: The long-term goal of this research is to develop and investigate abstracted models that are consistent with the constraints owing to the nonlinear, dissipative and open nature of the nearshore. Model development takes place within the framework of the nearshore as a hierarchical complex system wherein the behavior of the emerging form is related to a restricted number of variables that dominate the faster scale dynamics of the constituents.

A new technique for near real‐time optical imaging of surf zone morphology, synoptic imaging, implemented at Scripps Beach, La Jolla, California, permits simultaneous measurements of the time‐varying position of individual linear and lunate megaripples, fields of bed forms, rocks, cobble patches, beach steps and sandbars, and troughs. A varying threshold filter for brightness is applied to video frames sampled at 1 Hz to remove pixels corresponding to surface foam and suspended bubbles or sediment. Remaining fragments of the video frames are averaged over time intervals generally ranging from 5 to 10 min to produce images of the surf zone sand bed. To facilitate accurate measurement of the position of sand bed features, these images are enhanced to increase feature visibility, transformed to plan view, and corrected for refraction using surveyed bathymetry and tide level. Contrast in the images results from differences in water depth, shading variations from tilted bed surfaces, and changes in bed material. The surveyed positions of megaripples and sandbars correspond to the positions of persistent features in the images. A ray path model quantifying sand bed contrast as a function of water depth, angle of line‐of‐sight, and light attenuation coefficient in water predicts that for the Scripps Beach field site, bed forms with height as small as 0.03–0.2 m can be detected in water depths up to 2.5 m, in accord with observations, and that visibility can be improved by changing the line of sight toward overhead viewing. Bed visibility is reduced by persistent surface foam and water turbidity generated by waves with period <8 s and height exceeding 1.5 m. Example images showing transitions between linear and lunate megaripples, location of megaripple crestlines, and the interaction between sandbars, bed form fields, and cobble patches illustrate the potential of synoptic imaging.

Striking circular, labyrinthine, polygonal, and striped patterns of stones and soil self-organize in many polar and high alpine environments. These forms emerge because freeze-thaw cycles drive an interplay between two feedback mechanisms. First, formation of ice lenses in freezing soil sorts stones and soil by displacing soil toward soil-rich domains and stones toward stone-rich domains. Second, stones are transported along the axis of elongate stone domains, which are squeezed and confined as freezing soil domains expand. In a numerical model implementing these feedbacks, circles, labyrinths, and islands form when sorting dominates; polygonal networks form when stone domain squeezing and confinement dominate; and stripes form as hillslope gradient is increased.